Abstract
Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem AX approximate to B with multiple right-hand sides can be revealed through the so-called core problem reduction; see [I. Hnetynkova, M.
Plesinger, and Z. Strakos, SIAM J.
Matrix Anal. Appl., 34 (2013), pp. 917-931].
The total least squares (TLS) serves as an important example of such approximation problem. Solvability of TLS was discussed in the full generality in [I.
Hnetynkova et al., SIAM J. Matrix Anal.
Appl., 32 (2011), pp. 748-770]. This theoretical study investigates solvability of core problems with multiple right-hand sides in the TLS sense.
It is shown that, contrary to the single right-hand side case, a core problem with multiple right-hand sides may not have a TLS solution. Further possible internal structure of core problems is studied.
Outputs of the classical TLS algorithm for the original problem AX approximate to B and for the core problem within AX approximate to B are compared.